2x(4-x)=5-x

Solution for 2x(4-x)=5-x equation:

2x(4-x)=5-x

We move all terms to the left:

2x(4-x)-(5-x)=0

We add all the numbers together, and all the variables

2x(-1x+4)-(-1x+5)=0

We multiply parentheses

-2x^2+8x-(-1x+5)=0

We get rid of parentheses

-2x^2+8x+1x-5=0

We add all the numbers together, and all the variables

-2x^2+9x-5=0

a = -2; b = 9; c = -5;
Δ = b2-4ac
Δ = 92-4·(-2)·(-5)
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{41}}{2*-2}=\frac{-9-\sqrt{41}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{41}}{2*-2}=\frac{-9+\sqrt{41}}{-4}
$